New topologies for genetic search space

Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation

Yoon

Moraglio

et al. 2006

Self Cite

Geometric crossover is a representation-independent generalization of the traditional crossover defined using the distance of the solution space. Using a distance tailored to the problem at hand, the formal definition of geometric crossover allows to design new problem-specific crossovers that embed problem-knowledge in the search. The standard encoding for multiway graph partitioning is highly redundant: each solution has a number of representations, one for each way of labeling the represented partition. Traditional crossover does not perform well on redundant encodings. We propose a new geometric crossover for graph partitioning based on a labeling-independent distance that filters the redundancy of the encoding. A correlation analysis of the fitness landscape based on this distance shows that it is well suited to graph partitioning. Our new genetic algorithm outperforms existing ones.

Section: Labeling-independent Distancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Geometric crossover for multiway graph partitioning

Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation

Yoon

Moraglio

et al. 2006

Self Cite

“…A study of the problem space [15] hints why improving the performance of genetic partitioning algorithm by reordering on random graphs is hard.…”

Section: Results Of Bisectionmentioning

confidence: 99%

Multi-attractor gene reordering for graph bisection

Hwang

Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation

Moon

2006

Self Cite

We propose a new gene reordering scheme for the graph bisection problem. Our gene reordering starts with two or more vertices to capture the clustering structure of graphs effectively. We devised a chromosome repairing method for hybrid genetic search, which helps exploit clusters when combined with gene reordering. Experimental tests showed that the suggested reordering scheme significantly improves the performance of genetic algorithms over previous reordering methods.

“…For this problem, a normalization method was used in [7,18]. In the sense that normalization pursues the minimization of genotype inconsistency among parental chromosomes (position-wise mismatches), in [20], Kim and Moon proposed an optimal, efficient normalization method for grouping problems based on a novel distance measure, the labeling-independent distance, that eliminates dependency on the underlying labeling completely. In the following, we show that, in effect, the recombination that includes the normalization procedure followed by standard crossover on discrete vectors, is an instance of quotient geometric crossover.…”

Section: Groupingsmentioning

confidence: 99%

Quotient geometric crossovers and redundant encodings

Yoon

Theoretical Computer Science

Moraglio

et al. 2012

Self Cite

We extend a geometric framework for the interpretation of search operators to encompass the genotype-phenotype mapping derived from an equivalence relation defined by an isometry group. We show that this mapping can be naturally interpreted using the concept of quotient space, in which the original space corresponds to the genotype space and the quotient space corresponds to the phenotype space. Using this characterization, it is possible to define induced geometric crossovers on the phenotype space (called quotient geometric crossovers). These crossovers have very appealing properties for non-synonymously redundant encodings, such as reducing the size of the search space actually searched, removing the low locality from the encodings, and allowing a more informed search by utilizing distances better tailored to the specific solution interpretation. Interestingly, quotient geometric crossovers act on genotypes but have an effect equivalent to geometric crossovers acting directly on the phenotype space. This property allows us to actually implement them even when phenotypes cannot be represented directly. We give four example applications of quotient geometric crossovers for non-synonymously redundant encodings and demonstrate their superiority experimentally.